Re: How can a Photon possess momentum without having mass?

Photons have zero *rest* mass, but that isn't the same as having no
mass.  In Special Relativity, mass is not a fixed quantity, but depends
on the motion of an object relative to an observer.  Out of this falls
the famous relation E = m c^2, where E is the total energy of an object,
m is its total mass, and c is the speed of light.  An object that emits
light does lose mass in the process, but because c^2 is a very big number,
the fractional mass loss tends to be small.

On a more advanced tack, you can show that the "length" of the momentum
4-vector is E^2 - (p c)^2 = (m_0 c^2)^2, where p is the momentum and
m_0 is the rest mass.  This is a relativistic invariant, which means
that all inertial observers (i.e., everyone who isn't accelerating)
calculate the same quantity for this "length"; this might be viewed
as the relativistic definition of "rest mass".  Plug in that the
photon has zero rest mass, and you get E = p c.  Also note that
E = h nu = h c/lambda, and you get the de Broglie relation.